What is the integral of (sin(x))/(cot(x)) ?

The integral of (sin(x))/(cot(x)) is -sin(x)+ln|tan(x)+sec(x)|+C

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integral of (sin(x))/(cot(x))

\int \frac{sin ( x )}{cot ( x )} d x

- sin (x) + ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int \frac{sin ( x )}{cot ( x )} d x

Apply Integration By Parts

: - sin (x) - \int - sec (x) d x

= - sin (x) - \int - sec (x) d x

\int - sec (x) d x = - ln ∣ tan (x) + sec (x) ∣

= - sin (x) - (- ln ∣ tan (x) + sec (x) ∣)

Simplify

= - sin (x) + ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= - sin (x) + ln ∣ tan (x) + sec (x) ∣ + C

\frac{s}{s ^{2} - 16}

y^{^{'}} = x^{2} - y - 2, y (0) = 1

\int \frac{x ^{2}}{( x ^{2} - 2 x + 2 ) ^{2}} d x

\frac{d}{d x} (ln (7 x^{3}))

(x^{2} + y + y^{2}) d x = x d y

What is the integral of (sin(x))/(cot(x)) ?
The integral of (sin(x))/(cot(x)) is -sin(x)+ln|tan(x)+sec(x)|+C